{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:PHG6NZSSFTOEFG3EWUXLH7QR2M","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f6ea27fb36ca077a7a8127cf4c8651fa89d0802d471fa1ba502e4f4004928bec","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2021-09-05T15:03:33Z","title_canon_sha256":"e1055c9ba809c7a2d343d6bf060469f3cf9e9b89198727bbf953539fbe0985d5"},"schema_version":"1.0","source":{"id":"2109.02093","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.02093","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2109.02093v3","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.02093","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"PHG6NZSSFTOE","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"PHG6NZSSFTOEFG3E","created_at":"2026-07-05T06:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"PHG6NZSS","created_at":"2026-07-05T06:04:32Z"}],"graph_snapshots":[{"event_id":"sha256:ffc16a7194450981207764ca4ecdf61616451fcadd342da544b84c2229db3491","target":"graph","created_at":"2026-07-05T06:04:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.02093/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class $\\mathcal{C}^{1,1}$, or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The f","authors_text":"Boris Mordukhovich, Dat Ba Tran, Pham Duy Khanh, Vo Thanh Phat","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2021-09-05T15:03:33Z","title":"Globally Convergent Coderivative-Based Generalized Newton Methods in Nonsmooth Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.02093","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d156ccffcae1c69d3259c75eb09c18bb94f64150a04d1c59995715392a18a7bd","target":"record","created_at":"2026-07-05T06:04:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f6ea27fb36ca077a7a8127cf4c8651fa89d0802d471fa1ba502e4f4004928bec","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2021-09-05T15:03:33Z","title_canon_sha256":"e1055c9ba809c7a2d343d6bf060469f3cf9e9b89198727bbf953539fbe0985d5"},"schema_version":"1.0","source":{"id":"2109.02093","kind":"arxiv","version":3}},"canonical_sha256":"79cde6e6522cdc429b64b52eb3fe11d32909b9c0dc9ff8e42752e4cf31de196c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79cde6e6522cdc429b64b52eb3fe11d32909b9c0dc9ff8e42752e4cf31de196c","first_computed_at":"2026-07-05T06:04:32.282761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:04:32.282761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sTnQTNryMz430G6DsMgd6Mh6YSKbOVlvray6d/YmTW8fI/REyqa2YFujLH+lsaP9HOPkDZpQ1UbjnlfTPF7dBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:04:32.283120Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.02093","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d156ccffcae1c69d3259c75eb09c18bb94f64150a04d1c59995715392a18a7bd","sha256:ffc16a7194450981207764ca4ecdf61616451fcadd342da544b84c2229db3491"],"state_sha256":"1e6f8d88a907cd342010879b708273c2ea58ff033c2d6f41e2e69195cd8309c2"}